Holographic mutual information and distinguishability of Wilson loop and defect operators
arXiv:1407.8191 · doi:10.1007/JHEP02(2015)100
Abstract
The mutual information of disconnected regions in large gauge theories with holographic gravity duals can undergo phase transitions. These occur when connected and disconnected bulk Ryu-Takayanagi surfaces exchange dominance. That is, the bulk `soap bubble' snaps as the boundary regions are drawn apart. We give a gauge-theoretic characterization of this transition: States with and without a certain defect operator insertion -- the defect separates the entangled spatial regions -- are shown to be perfectly distinguishable if and only if the Ryu-Takayanagi surface is connected. Meanwhile, states with and without a certain Wilson loop insertion -- the Wilson loop nontrivially threads the spatial regions -- are perfectly distinguishable if and only if the Ryu-Takayanagi surface is disconnected. The quantum relative entropy of two perfectly distinguishable states is infinite. The results are obtained by relating the soap bubble transition to Hawking-Page (deconfinement) transitions in the Renyi entropies, where defect operators and Wilson loops are known to act as order parameters.
arXiv comment1+21 pages. 11 figures
References in corpus (22)
- The Large N Limit of Superconformal Field Theories and Supergravity
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Wilson loops in large N field theories
- Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
- Towards a derivation of holographic entanglement entropy
- Generalized gravitational entropy
- Quantum corrections to holographic entanglement entropy
- Complexity and Shock Wave Geometries
- Open and Closed String Interpretation of SUSY CFT's on Branes with Boundaries
- Entanglement Renyi entropies in holographic theories
- Holography and Defect Conformal Field Theories
- Relative Entropy and Holography
- A holographic proof of the strong subadditivity of entanglement entropy
- Entanglement Entropy at Large Central Charge
- Exact results for the entanglement entropy and the energy radiated by a quark
- Holographic entanglement beyond classical gravity
- Wilson Loops in Large N Theories
- The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT
- Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects
- Entanglement Entropy for Probe Branes
- Generalized gravitational entropy of probe branes: flavor entanglement holographically
- An Operator Product Expansion for the Mutual Information in AdS/CFT